1. Field of the Invention
The present invention relates to a photonic crystal waveguide which can be used as a basic structure which forms photonic devices such as lasers and photonic ICs used for optical information processing, optical transmission and the like.
2. Description of the Related Art
In a conventional photonic device, since light confinement is carried out by using difference of refractive indices, a space for light confinement must be large. Therefore, the device can not be configured very small. In addition, when a steeply bent waveguide is used in order to increase the scale of integration of the device, scattering loss occurs. Thus, it is difficult to integrate photonic circuits and it is difficult to downsize the photonic device. As a result, the size of the photonic device is much larger than that of an electric device. Therefore, the photonic crystal is expected to be a new photonic material which can solve the above-mentioned problem, in which the photonic crystal can perform light confinement by a concept completely different from the conventional one.
The photonic crystal has an artificial multidimensional periodic structure in which periodicity, which is almost the same as light wavelength, is formed by using more than one kinds of mediums having different refractive indices, and the photonic crystal has a band structure of light similar to a band structure of electron. Therefore, forbidden band of light (photonic band-gap) appears in a specific structure so that the photonic crystal having the specific structure functions as a nonconductor for light.
It is theoretically known that, when a line defect which disturbs periodicity of the photonic crystal is included in the photonic crystal, an optical waveguide which completely confines light and has a waveguiding mode in a frequency region of the photonic band-gap can be realized (J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Photonic Crystal: putting a new twist on light, Nature 386,143 (1997)). J. D. Joannopoulos and others applied a line defect in a two-dimensional photonic crystal in which cylindrical columns having large refractive index almost the same as that of a semiconductor are arranged on a square lattice of lattice constant xe2x80x9caxe2x80x9d which is about light wavelength and the radius of each cylindrical column is a/5, and, J. D. Joannopoulos and others theoretically indicated that an optical waveguide having no scattering loss even when it is steeply bent can be realized. This waveguide can be very important for realizing a large scale integrated optical circuit.
In order to realize the optical waveguide for forming the large scale integrated optical circuit, it is necessary to realize a single waveguiding mode in the photonic band-gap frequency band. When a multi-mode waveguide having a plurality of modes is used as a bent waveguide, there is a problem, for example, in that a part of mode may be converted into a different mode in a bending part. Thus, the multi-mode waveguide can not be used as an effective bent waveguide necessary for realizing the large scale integrated optical circuit. That is the reason for requiring the single-mode. In addition, the multi-mode waveguide is not suitable for high-speed communication.
Some types of waveguides have been manufactured. In the various waveguides, waveguides using the two-dimensional photonic crystal is promising since it is very difficult to fabricate waveguides by a three-dimensional photonic crystal which has full band-gap.
When using the two-dimensional photonic crystal for the waveguide, it is necessary to confine light in the direction perpendicular to the two-dimensional plane. Several methods has been proposed as the method of light confinement. In the methods, using a two-dimensional photonic crystal slab on oxide cladding is preferable since a structure having a large area can be easily manufactured by the two-dimensional photonic crystal slab on oxide cladding and it is easy to add various function elements in the same structure. The two-dimensional photonic crystal slab on oxide cladding is based on a structure in which a thin semiconductor film of high refractive index (from 3 to 3.5) is deposited on a dielectric of low refractive index (oxide or polymer in many cases, the refractive index is about 1.5).
In addition, a substrate called Silicon-On-Insulator (SOI) substrate is being applied to LSIs, and high-quality SOI substrate can be manufactured in recent years. The SOI substrate is formed by providing a silicon (Si) thin-film on silica (SiO2). By using the SOI substrate, there is a merit that the two-dimensional photonic crystal slab on oxide cladding having high quality can be easily manufactured. The merit can not be obtained by using other structures (for example, two-dimensional photonic crystal air-bridge slab in which cladding of both sides is air).
As mentioned above, the two-dimensional photonic crystal slab on oxide cladding has the advantage of being easier to manufacture than the two-dimensional photonic crystal air-bridge slab and the like. However, the structure has following problems so that the single waveguiding mode was not realized in the photonic band-gap frequency band according to the conventional structure.
In waveguiding modes generated by the line defect in the optical waveguide of the two-dimensional photonic crystal slab, light is strongly confined in the directions of the two-dimensional plane by the photonic band-gap and scattering loss does not exist in the directions. However, light is generally leaky in a high frequency region above a light line of cladding, that is, the light may be leaked to the cladding. (The light line represents the lowest frequency, with respect to propagation constant, by which light can transmit in the cladding, and, the light line can be represented by a line defined by w=ck/n (w: angular frequency, c: light speed, n: refractive index, k: wave number).) Therefore, it is customary to use a low frequency region below the light line such that the waveguide light does not leak to cladding layers of both sides.
FIGS. 1A and 1B are schematic diagrams of a structure of a single missing-hole line defect photonic crystal waveguide of a typical air-hole type according to a conventional technology. FIG. 1A shows a top view and FIG. 1B shows a B-Bxe2x80x2 section view. The conventional single missing-hole line defect photonic crystal waveguide can be also called as a normal two-dimensional photonic crystal slab waveguide in this specification. In FIGS. 1A and 1B, 5 indicates an optical waveguide part, 2 indicates an Si layer, 3 indicates an SiO2 layer which is a cladding layer, and 4 indicates an air-hole triangle lattice point, in which the lattice constant is represented as xe2x80x9caxe2x80x9d. Each air-hole is a cylindrical column or a polygon column which penetrates the Si layer 2. The diameter of the air-hole is 0.215 xcexcm in this example. In the air-hole triangle lattice, the air-hole is placed in each lattice point of the triangle lattice. The triangle lattice is a regular lattice in which lattice points are placed on vertices of regular triangles which are arranged over the two-dimensional plane.
As representative two-dimensional photonic crystals having the photonic band-gap, there are two structures. One is a structure in which columns of high refractive index are provided in air. Another is a structure in which air-holes are provided in a high refractive index layer like the above-mentioned example. (The air-hole can be also called a low refractive index column or a low refractive index cylindrical column.) The former structure, which was used by J. D. Joannopoulos and others, requires a cladding layer for supporting the columns. Since the refractive index of the cladding layer is larger than that of the air which is a core for the line defect waveguide, very long columns are necessary for preventing light leakage to the upper and lower sides so that manufacturing such structure becomes very difficult. On the other hand, as for the latter structure, since the air-hole can stand by itself, the cladding layer can be freely chosen, and it is easy to determine a core having refractive index larger than that of the cladding layer. Thus, limitation on manufacturing is small so that it is easy to select structural condition that light hardly leak to the upper and lower sides.
In addition, although the holes can be placed on the two-dimensional plane of the high refractive index plate of the photonic crystal in various way, a structure in which the holes (cylindrical columns or polygon columns) are arranged in a triangle lattice pattern is known to have the photonic band-gap ranging over a wide frequency band. This means that this structure functions as a nonconductor for light in wide frequency band. This structure is preferable since frequency can be selected from wide rage frequencies when designing a waveguide.
FIG. 2 shows a dispersion relation of waveguiding modes of a conventional typical single missing-hole line defect photonic crystal waveguide. When such waveguide is formed by using the two-dimensional photonic crystal slab on oxide cladding, the waveguiding modes become as shown in FIG. 2. In the figure, normalized frequency represented by (lattice constant/wavelength) which is a dimensionless number is used. In addition, normalized propagation constant represented by (wave numberxc3x97lattice constant/2xcfx80) is used. The light line of the cladding (SiO2, refractive index 1.46) is also shown in FIG. 2.
In the conventional structure shown in FIG. 2, the waveguiding mode which satisfies the condition that light does not leak to the cladding layer is only in a region circled by an ellipse which is below the light line. However, inclination of the waveguiding mode in the region is very small so that group velocity (energy propagation velocity) of the waveguiding mode, which is determined depending on the inclination, is very small. There are many problems for using the waveguide having the waveguiding mode of very small group velocity since time for light transmission becomes long. In addition, since heterogeneity exist in an actual structure to some extent, the mode of very small group velocity is affected by the heterogeneity so that light may not propagate. In addition, in the mode above the light line (high frequency region), light can not propagate since diffraction loss in the photonic crystal is too large. That is, light in the photonic crystal waveguide propagates while being perturbed by periodic structure of the photonic crystal, and light leaks to the cladding layer by diffraction loss in the mode above the light line.
The inventors actually manufactured the conventional single missing-hole line defect photonic crystal waveguide. However, light propagation was not detected at all. The cause of the problem is that there is no realistically usable waveguiding mode which has a group velocity which is not too small below the light line, and that the diffraction loss is very large in the region above the light line.
In order to use the mode below the light line, it is necessary to move the light line upward or to move the waveguiding mode appropriately in the graph of FIG. 2. However, as long as the oxide cladding structure is used, since the position of the light line is determined by the refractive index of the cladding, the position of the light line can not be changed largely. As for the waveguiding mode, as long as the single-mode within the band-gap should be used, it is difficult to obtain a waveguiding mode having large group velocity below the light line by using the structure shown in FIG. 1. As for crystal structures other than the triangle lattice such as square lattice, it is more difficult to obtain such waveguiding mode. Therefore, it is very difficult to use waveguiding modes below the light line.
The conventional technology will be described further from another viewpoint in the following.
FIGS. 3A-3C are figures for explaining the conventional single missing-hole line defect photonic crystal waveguide (optical waveguide). FIG. 3A shows a top view of the optical waveguide, FIG. 3B shows an A-Axe2x80x2 section view, and FIG. 3C shows a B-Bxe2x80x2 section view.
In FIG. 3A, the optical waveguide 30 includes dielectric thin-film slab 31 (which corresponds to the above-mentioned high refractive index plate) sandwiched between a top cladding layer 36 and a bottom cladding layer 37. A photonic crystal structure is formed in the dielectric thin-film slab 31 by providing low refractive index cylindrical columns 35 having lower refractive index than that of the dielectric thin-film slab 31 in a triangle lattice pattern. In addition, one line of the low refractive index cylindrical columns 35 is replaced by a dielectric having the same refractive index as the dielectric thin-film slab 31 such that the part of the one line can be used as an optical waveguide part 32. Arrows ←xe2x86x92 in the optical waveguide part 32 indicate optical propagation directions. The waveguide shown in FIG. 1 is an example of a structure shown in FIG. 3 in which the top cladding layer 36 and the low refractive index cylindrical column 35 are air, the bottom cladding layer 37 is SiO2, and the dielectric thin-film slab 31 is Si.
Here, it is assumed that refractive indices of the dielectric thin-film slab 31, the low refractive index cylindrical column 35, the top cladding layer 36 and the bottom cladding layer 37 are n1=3.5, n2=1.0, n3=n4=1.46 respectively, and that radius of the low refractive index cylindrical column 35 is 0.275a and thickness of the dielectric thin-film slab 31 is 0.50a, in which xe2x80x9caxe2x80x9d represents the lattice constant (triangle lattice in this example) of the photonic crystal. The low refractive index cylindrical column 35 having the refractive index 1.0 is the same as an air-hole. Characteristics of the optical waveguide 30 will be described in the following.
These refractive indices of the optical waveguide 30 correspond to those of Si, air (vacuum) and SiO2 which are often used for forming waveguides targeted for infrared light for optical communication having a wavelength about 1.55 xcexcm.
Since a relative dielectric constant corresponds to a square of refractive index, xe2x80x9crelative dielectric constantxe2x80x9d or xe2x80x9cdielectric constantxe2x80x9d can be used instead of xe2x80x9crefractive indexxe2x80x9d in this specification.
FIGS. 4A-4C are figures for explaining waveguiding modes of the above-mentioned optical waveguide. FIG. 4A shows dispersion curves of waveguiding modes which can propagate through the optical waveguide part. The dispersion curves of waveguiding modes are obtained by using a plane wave expansion method (R. D. Meade et al., Physical Review B 48,8434 (1993)) to which periodic boundary condition is applied. This figure is similar to FIG. 2. FIG. 4B shows magnetic field component perpendicular to the dielectric thin-film slab according to a mode 1 in FIG. 4A, and FIG. 4C shows magnetic field component perpendicular to the dielectric thin-film slab according to a mode 2 in FIG. 4A.
Each amount in FIG. 4A is normalized by the lattice constant or speed of light c. The diagonally shaded regions correspond to the outside of photonic band-gap (J D. JoannoPoulos, R D. Meade, J N. Winn, xe2x80x9cPhotonic Crystalsxe2x80x9d, Princeton University Press, Princeton (1995)), that is, the diagonally shaded areas show regions in which light can not be confined in the optical waveguide part 32 (A. Mekis et al., Physical Review B 58,4809 (1998)).
In the vertical line hatching region, power of light confinement caused by difference of refractive indices between the dielectric thin-film slab 31 and the top cladding layer 36/bottom cladding layer 37 is weakened so that light can not be confined in the optical waveguide part 32 (S G. Johnson et al., Physical Review B 60,5751 (1999)). The vertical line hatching region corresponds to the before-mentioned above region of the light line. That is, a region to be considered used for the waveguide is only a white region in FIG. 4A.
As is understood by the figure, two waveguiding modes 1 and 2 exist in the white region of the conventional optical waveguide 30. Further waveguiding modes may exist when the band-gap is wider, however, the two modes 1 and 2 will be considered here for the sake of simplicity. The mode 1 corresponds to the mode circled by the ellipse in FIG. 2, and the mode 2 corresponds to the mode of upper dotted line.
In these two modes 1 and 2, the mode 1 in the low frequency side generally has magnetic field distribution shown in FIG. 4B, and the mode 2 in the high frequency side generally has magnetic field distribution shown in FIG. 4C.
In these waveguiding modes 1 and 2, the mode 1 is practical since the mode 1 has electric field distribution almost the same as that of a general single-mode waveguide. On the other hand electric field distribution of the mode 2 is largely different from that of the general signal-mode waveguide. Therefore, it is difficult to conduct light from an outside circuit by using the mode 2. That is, the mode 2 is not a practical waveguiding mode. In addition, in the same way, it is clear, from general argument of waveguide, that waveguiding modes of higher frequency side which appears when the band-gap is wide is not practical since the waveguiding mode is largely different from that of the general single-mode waveguide.
Thus, the mode 1 is used for the conventional waveguide. However, as is known from FIG. 4A, since the frequency hardly change even when the propagation constant change in this mode 1, the mode 1 has a defect that usable frequency band is very small. In this example, the frequency band is about 1%.
The fact that the frequency hardly change even when the propagation constant change means that the group velocity of the waveguiding mode is very low. Therefore, the conventional waveguide has a defect that transmission time becomes very long, and propagation loss due to absorption and scattering loss in waveguide becomes large.
An object of the present invention is to solve the above-mentioned problems in the photonic crystal waveguide and to provide a two-dimensional photonic crystal slab waveguide allowing single-mode transmission in which group velocity is increased and propagation loss is decreased.
The above object can be achieved by a two-dimensional photonic crystal slab waveguide in which a part of holes in a lattice structure of a two-dimensional photonic crystal slab do not exist linearly so that a line defect is formed, wherein:
a first width which is a distance between centers of nearest two lattice points located on both sides of the line defect is different from a second width which is a distance between centers of nearest two lattice points located on both sides of a line defect in a normal two-dimensional photonic crystal slab waveguide which simply lacks holes of a single line.
In the two-dimensional photonic crystal slab waveguide, the first width may a value from 0.5 times to 0.85 times of the second width.
According to the invention, since the first width which is a distance between centers of nearest two lattice points located on both sides of the line defect is different from the second width which is a corresponding distance in a normal two-dimensional photonic crystal slab waveguide, an optical waveguide which can form a single waveguiding mode having large group velocity below the light line can be provided. The two-dimensional photonic crystal slab waveguide may be called a single missing-hole line defect photonic crystal waveguide.
In the two-dimensional photonic crystal slab waveguide, the lattice structure may be formed by air-hole triangle lattices, and the two-dimensional photonic crystal slab waveguide may include an oxide cladding or a polymer cladding. In addition, the two-dimensional photonic crystal slab waveguide may be formed by using a Silicon-On-Insulator (SOI) substrate.
In the two-dimensional photonic crystal slab waveguide, the first width may be wider than the second width in which a single-mode appears in a high frequency side of a light line of cladding in a dispersion relation of waveguiding modes of the two-dimensional photonic crystal slab waveguide having the first width, and the first width may a value from 1.3 times to 1.6 times of the second width.
According to the invention, an optical waveguide can be provided which can form a single waveguiding mode of low loss above the light line can be provided.
The above object can be also achieved by a two-dimensional photonic crystal slab waveguide in which dielectric cylindrical or polygon columns having lower refractive index than that of a dielectric thin-film slab are provided in the dielectric thin-film slab in a two-dimensional lattice pattern, and the dielectric thin-film slab is sandwiched by a top cladding layer and a bottom cladding layer which have lower refractive index than that of the dielectric thin-film slab, wherein:
positions of dielectric columns which form one line of the lattice of two-dimensional photonic crystal slab for an optical waveguide part are shifted in an optical propagation direction.
That is, the dielectric columns in an optical waveguide part in the two-dimensional photonic crystal slab waveguide are located at positions which are shifted in an optical propagation direction from positions at which the dielectric columns should be positioned in a normal two-dimensional photonic crystal slab.
Also according to the invention, an optical waveguide which can form a single waveguiding mode having large group velocity below the light line can be provided. The dielectric cylindrical or polygon columns, or the dielectric columns are low refractive index columns having lower refractive index than that of the dielectric thin-film slab.
In the two-dimensional photonic crystal slab waveguide, a first diameter of the dielectric columns in the optical waveguide part may be different from a second diameter of other dielectric columns located in parts other than the optical waveguide part, and the first diameter is a value by which the dielectric columns does not contact with the other dielectric columns.
In addition, in the two-dimensional photonic crystal slab waveguide, positions of dielectric columns which form one line of the lattice of two-dimensional photonic crystal slab for an optical waveguide part may be shifted in an optical propagation direction by a half of the lattice constant of the normal two-dimensional photonic crystal slab.
That is, each dielectric column of dielectric columns in the optical waveguide part may be apart from a position at which the each dielectric column should be positioned in the normal two-dimensional photonic crystal slab by a half of the lattice constant of the normal two-dimensional photonic crystal slab.
In the two-dimensional photonic crystal slab waveguide, the dielectric cylindrical or polygon columns may be arranged in a triangle lattice pattern having a lattice constant xe2x80x9caxe2x80x9d, a radius or a half-breadth of the dielectric cylindrical or polygon columns is from 0.2a to 0.45a, and the radius or half-breadth is determined such that the dielectric cylindrical or polygon columns do not contact with dielectric columns in the optical waveguide part.
In the two-dimensional photonic crystal slab waveguide, a refractive index of the dielectric thin-film slab may be from 3.0 to 4.5, and each of refractive indices of parts other than the dielectric thin-film slab may be from 1.0 to 1.7.
In addition, in the two-dimensional photonic crystal slab waveguide, the dielectric cylindrical or polygon columns may be arranged in a square lattice pattern having a lattice constant xe2x80x9caxe2x80x9d, a radius or a half-breadth of the dielectric cylindrical or polygon columns is from 0.35a to 0.45a, and the radius or half-breadth is determined such that wherein the dielectric cylindrical or polygon columns do not contact with dielectric columns in the optical waveguide part.
Further, in the two-dimensional photonic crystal slab waveguide, silicon, germanium, gallium arsenide base compound, indium phosphide base compound, or indium antimony base compound may be used as a material of the dielectric thin-film slab, and silica, polyimide base organic compound, epoxy base organic compound, acrylic base organic compound, air or vacuum may be used as a material of parts other than the dielectric thin-film slab.